Abstract [en]

The objective of this work is to reconstruct a 3D model of the planetary nebula (PN) NCG 6781 using the computer software SHAPE.

A planetary nebula forms when specific types of stars, with masses between 0.8-8 M⊙ (where ⊙ is solar masses) end their lives. In the last evolutionary stage of these stars radial pulsations and a fast wind blows away the spherical, outer layers of the star until only the core of the star remains. The core will cool off and finally becomes a so called white dwarf which is surrounded by a shell of the ejected gas and dust. This expanding shell of glowing ionized gas and dust is called a planetary nebula. The word "nebula" is Latin for mist or cloud and the name planetary nebula came in the 1780’s since these objects looked like large gaseous planets when observed. Planetary nebulae exist in many and various shapes, from bipolar to multistructured. It is anticipated that the fast wind in combination with radiation from the star affects the formation of the planetary nebulae. Exactly how these processes work and what mechanisms that cause the outer, spherical layers of the star to adapt the spectacular and multi-structured shapes seen in planetary nebulae is not well known.

SHAPE is an interactive computer program that has been developed during the last few years and is a tool used by astrophysicists. In SHAPE, 3D models of different astronomical objects can be set up in order to understand and try to determine their morphology, density and temperature distribution and velocity field. SHAPE is particularly suited for planetary nebulae. The aim of a 3D model is that it provides an opportunity to rotate the object and view it from different angles and determine how the velocity field affects the emission from the nebula. This gives new insights to the structure of the object and its distribution, which may contribute to increased knowledge about the mechanisms that control the formation of planetary nebulae.

In this work I have modeled the planetary nebula NGC 6781. I compare my model to previous attempts at determining the morphology of the nebula and to recently obtained observations of the carbon monoxide (CO) emission from the nebula. The model of NGC 6781 appears to be a hollow cylinder with inner radius 38” and outer radius 60” and with a depth of 117”. The model is a bit extended at the waist so it gets the shape of a barrel. The cylinder is tilted forward 21 degrees and rotated to the left with 20 degrees. The expanding gas within the nebula is moving radially outwards with the relation v=0.26·r, where r is the distance from the origin and the gas has a velocity of ∼ 16 km/s at the rim of the cylinder. The model reproduces the observed CO emission well and in particular the velocity, temperature and density distribution of the molecular gas. The velocity, temperature and density distribution agrees with typical values found for PNe and with what could be expected if NGC 6781 has evolved from an AGB star.

It is hard to estimate exact errors for the different parameters since they are strongly dependent on one another. It seems like the velocity and den- sity parameters are those most sensitive to variations and these causes the biggest changes in the model, when altered.